BuoyancyHardQuestion 30911
Question
A hollow sphere of outer radius R, inner radius r, and material density ρ_s just floats in water (density ρ_w). The relation is:
- Aρ_s(R³−r³) = ρ_w R³Correct
- Bρ_s R³ = ρ_w(R³−r³)
- Cρ_s r³ = ρ_w R³
- Dρ_s(R³+r³) = ρ_w R³
Correct answer
ρ_s(R³−r³) = ρ_w R³
Explanation
Weight of shell = ρ_s × (4π/3)(R³−r³)g. Buoyant force = ρ_w × (4π/3)R³g. Setting equal: ρ_s(R³−r³) = ρ_w R³.